- #1

EugP

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## Homework Statement

I'm taking a Magnetic Fields class, and the professor taught us doing cross and dot products using the permutation index. But I don't quite understand how it works completely.

I have these problems:

Given:

[tex]\vec A=\hat x + 2\hat y - 3\hat z[/tex]

[tex]\vec B=3\hat x - 4\hat y[/tex]

[tex]\vec C=3\hat y - 4\hat z[/tex]

Find:

1) [tex]\vec A \times \vec C[/tex]

2) [tex]\hat x \times \vec B[/tex]

## Homework Equations

## The Attempt at a Solution

1) Using what I know about the permitivity constant:

[tex](\vec A \times \vec C)=[/tex]

[tex]\varepsilon_{xyz}\vec A_y \vec C_z=[/tex]

But I don't know where to go from here. All I know is that [tex]\varepsilon_{xyz} = 1[tex] because indices are a cyclic permutation, but I don't know what to do next.

2) For this one I don't even know where to begin.

Please someone help, any help at all would be great.